# fitted.ppm

0th

Percentile

##### Fitted Conditional Intensity for Point Process Model

Given a point process model fitted to a point pattern, compute the fitted conditional intensity of the model at the points of the quadrature scheme used to fit the model.

Keywords
spatial
##### Usage
fitted.ppm(object, ..., type="lambda")
##### Arguments
object
The fitted point process model (an object of class "ppm")
...
Ignored.
type
String (partially matched) indicating whether the fitted value is the conditional intensity ("lambda") or the trend ("trend").
##### Details

The argument object must be a fitted point process model (object of class "ppm"). Such objects are produced by the model-fitting algorithm ppm).

This function evaluates the conditional intensity $\hat\lambda(u, x)$ or spatial trend $\hat b(u)$ of the fitted point process model for certain locations $u$, where x is the original point pattern dataset to which the model was fitted.

The locations $u$ at which the fitted conditional intensity/trend is evaluated, are the points of the quadrature scheme used to fit the model in ppm. They include the data points (the points of the original point pattern dataset x) and other dummy'' points in the window of observation.

Use predict.ppm to compute the fitted conditional intensity at other locations or with other values of the explanatory variables.

##### Value

• A vector containing the values of the fitted conditional intensity or (if type="trend") the fitted spatial trend. Entries in this vector correspond to the quadrature points (data or dummy points) used to fit the model. The quadrature points can be extracted from object by union.quad(quad.ppm(object)).

##### References

Baddeley, A., Moller, J. and Turner, R. (2004) Residuals for spatial point processes. In preparation.

ppm.object, ppm, predict.ppm

• fitted.ppm
##### Examples
data(cells)
str <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
lambda <- fitted(str)

# extract quadrature points in corresponding order
plot(quadmarked)